Les pages des membres du laboratoire Lagrange
Nicolas Besse
- Détails
Professor of Applied Mathematics [Sec. CNU 26]
office : Pavillon Henri Crétien (PHC Nord, Bureau PHCN-18), Mont-Gros [map]
adress : Laboratoire J.-L. LAGRANGE,
UMR CNRS/OCA/UCA 7293,
Observatoire de la Côte d'Azur,
Bd de l'Observatoire CS 34229,
06304 Nice Cedex 4, France
phone : +33 (0)4 92 00 31 13
fax : +33 (0)4 92 00 31 21
email : Nicolas.Besse@oca.eu
web : www.oca.eu/fr/nicolas-besse/
Curriculum Vitae
- Détails
Affiliation
Laboratoire J.-L. LAGRANGE (UMR CNRS/OCA/UCA 7293)
Observatoire de la Côte d'Azur
CS 34229, 06304 Nice Cedex 4, France
Education
- HdR (Habilitation à diriger des Recherches) in Applied Mathematics, Université Henri Poincaré Nancy I, 2009
- PhD in Applied Mathematics, Université Louis Pasteur Strasbourg I, 2003
- MSc (DEA) in Applied Mathematics, Université Paul Sabatier Toulouse III, 2000
- MSc (French "Grandes Écoles" Diploma) in Applied Mathematics, Dept. Génie Mathématique & Modélisation, Institut National des Sciences Appliquées, Toulouse, 2000
Employment
- Professor of Applied Mathematics, Observatoire de la Côte d'Azur, Nice, 2015–present
- Associate Professor (Maître de Conférence) of Applied Mathematics, Université de Lorraine, Nancy, 2005–2015
- INRIA Researcher Position in the Calvi Project-Team, Nancy, 2008–2010
- CNRS Researcher Position at LPMIA, Nancy, 2007–2008 (6 months), 2006–2007 (6 months)
- Postdoctoral Fellow at the Wolfgang Pauli Institute, Wien Universität, Vienna, 2004–2005 (6 months)
- French Teaching and Research Assistantship (ATER) at IRMA, Université Louis Pasteur Strasbourg I, Strasbourg, 2003–2004 (6 months)
- HYKE Postdoctoral Fellow at the Angewandte Mathematische Institut, Albert-Ludwigs Universität, Freiburg, 2003–2004 (6 months)
- CFR PhD Fellowship at the French Atomic Energy Commission, CEA DAM-Île-de-France, Bruyères-le-Châtel, 2000–2003
Areas of Experience
- Nonlinear Partial Differential Equations
- Kinetic and Multi-Fluids Equations
- Numerical Analysis, Scientific Computing
- Plasma Physics, Inertial and Magnetic Fusion, Plasma and Fluid Turbulence
Publications
Click here for a list of publications and preprints
Former Projects
- ANR VLASIX, Project on gravitational Vlasov equations, 2013-2017
- EUROFUSION 2015, Contract on gyrokinetic equations for magnetic fusion, 2015-2017
- INRIA Tonus, Project on tokamaks and numerical simulations, 2013-2015
- EUROFUSION 2014, Contract on gyrokinetic equations for magnetic fusion, 2014
- ANR GYPSI, Contract on gyrokinetic turbulence, 2010-2014
- LRC-EURATOM-CEA-Cadarache, Contract on magnetic fusion, 2005-2013
- INRIA Calvi, Project on scientific computing and visualization, 2003-2012
- INRIA AE Fusion, Contract on magnetic fusion, 2008-2012
- ANR EGYPT, Contract on gyrokinetic turbulence, 2007-2010
- ANR VLASOV, Contract on wave-particle interaction in Vlasovian plasmas, 2006-2009
- INRIA ARC Fusion, Contract on magnetic fusion, 2006-2007
Graduate Student Theses Supervised
- Swetha S. Kolluru, PhD 2024 of Physics of Indian Institut of Science Bengaluru, Chapter 3 "Novel spectral methods for CFD", IFCAM and UniCA-Jedi fellowships, advisor: R. Pandit.
- Frederik Moller, PhD 2023 of Engineering of Technische Universität Wien, Chapter 6 "Numerical methods for GHD", advisor: H.-J. Schmiedmayer.
- Tobias Hertel, PhD 2020 of Applied Mathematics of Université Côte d'Azur, MENRT Fellowship.
- Eric Madaule, PhD 2016 of Applied Mathematics of Université de Lorraine, ANR VLASIX Fellowship, co-advisor: E. Deriaz.
- David Coulette, PhD 2013 of Plasma Physics of Université de Lorraine, CNRS/Région–Lorraine Fellowship.
- Anaïs Crestetto, PhD 2012 of Applied Mathematics of Université de Strasbourg, Chapter 1 "Multi-water-bag models", advisors: P. Helluy, E. Sonnendrücker.
- Rudy Klein, PhD 2009 of Plasma Physics of Université Henri Poincaré, co-advised with P. Bertrand, E. Gravier.
- Pierre Morel, PhD 2008 of Plasma Physics of Université Henri Poincaré, co-advised with P. Bertrand, E. Gravier.
Former Postdocs Supervised
- Nicolas Dubuit (2009-2010) ANR EGYPT Postdoctoral Fellow, Assistant Professor of Plasma Physics, Université Aix-Marseille
Publications
- Détails
Papers submitted to refered international journals, preprints
- N. Besse, C. Cheverry,
Singular limits of anisotropic weak solutions to compressible magnetohydrodynamics,
submitted - N. Besse, C. Cheverry,
Asymptotic analysis of extended magnetohydrodynamics,
submitted - N. Besse,
Analysis of the spectral relaxation method and the spectral purging method for nonlinear conservation laws,
submitted
Papers published or accepted in refered international journals
- N. Besse, C. Cheverry,
The equations of extended magnetohydrodynamics,
accepted in SIAM Journal on Mathematical Analysis, 2025. PDF - S. Kollluru, N. Besse, R. Pandit,
Novel spectral methods for shock capturing and the removal of tygers in computational fluid dynamics,
J. Comput. Phys. 519 (2024) 113446. PDF - F. Moller, N. Besse, I. Mazets, H.-P. Stimming, N. Mauser,
The dissipative generalized hydrodynamic equations and their numerical solution,
J. Comput. Phys. 493 (2023) 112431. PDF - N. Besse,
Stochastic Lagrangian perturbation of Lie transport and applications to fluids,
Nonlinear Analysis 232 (2023) 113249. PDF - N. Besse,
Lagrangian regularity of the electron magnetohydrodynamics flow on a bounded domain,
J. Math. Anal. Appl. 511 (2022) 126076. PDF - C. Bardos, N. Besse,
About the derivation of quasilinear approximation in plasma physics,
Appl. Numeri. Harmon. Anal. 111 (2023) 247-279. PDF - T. Hertel, N. Besse, U. Frisch,
The Cauchy-Lagrange method for 3D-axisymmetric wall-bounded and potentially singular incompressible Euler flows,
J. Comput. Phys. 449 (2022) 110758. PDF - C. Bardos, N. Besse,
Diffusion limit of the Vlasov equation in the weak turbulent regime,
J. Math. Phys. 62 (2021) 101505. PDF - S.D. Murugan, U. Frisch, S. Nazarenko, N.Besse, S.S. Ray,
Suppressing thermalisation and constructing weak solutions in truncated inviscid equations of hydrodynamcis: Lessons from Burgers equation,
Phys. Rev. Research 2 (2020) 033202. PDF - N. Besse,
Regularity of the geodesic flow of the incompressible Euler equations on a manifold,
Commun. Math. Phys., 375 (2020) 2155-2189. PDF - C. Bardos, N. Besse, T.T. Nguyen,
Onsager type conjecture and renormalized solutions for the relativistic Vlasov-Maxwell system,
Quart. Appl. Math., 78 (2019) 163-217. PDF - N. Besse, P. Bechouche,
Regularity of weak solutions for the relativistic Vlasov-Maxwell system,
J. Hyperbolic Differ. Equ., 15 (2018) 693-719. PDF - N. Besse, U. Frisch,
Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces,
J. Fluid. Mech., 825 (2017), 412-478. PDF - D. Coulette, N. Besse,
Numerical resolution of the global eigenvalue problem for the gyrokinetic-waterbag model in toroidal geometry,
J. Plasma Phys., 83 (2017), 905830207. PDF - N. Besse, U. Frisch,
A constructive approach to regularity of Lagrangian trajectories for incompressible Euler flow in a bounded domain,
Commun. Math. Phys., 351 (2017), 689-707. PDF - N. Besse, E. Deriaz, E. Madaule,
Adaptive multiresolution semi-Lagrangian discontinuous Galerkin methods for the Vlasov equations,
J. Comput. Phys., 332 (2017), 376-417. PDF - N. Besse, D. Coulette,
Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry,
J. Math. Phys., 57 (2016), 081518. PDF - N. Besse,
Discontinuous Galerkin finite element methods for the gyrokinetic-waterbag equations,
IMA J. Numer. Anal., 37 (2017), 985-1040. PDF - C. Bardos, N. Besse,
Semi-classical limit of an infinite dimensional system of nonlinear Schrödinger equations,
Bull. Inst. Math. Acad. Sin., 11 (2016), 43-61. PDF - N. Besse,
Lagrangian averaged gyrokinetic-waterbag continuum,
Commun. Math. Sci., 14 (2016), 593-626. PDF - C. Bardos, N. Besse,
Hamiltonian structure, fluid representation and stability for the Vlasov-Dirac-Benney equation,
Fields Inst. Commun., 75 (2015), 1-30. PDF - P. Morel, F. Dreydemy Ghiro, V. Berionni, D. Coulette, N. Besse, O. Gurcan,
A Multi-water-bag model of drift-kinetic electron plasma,
Eur. Phys. J. D, 68 (2014), 220. PDF - C. Bardos, N. Besse,
The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits,
Kinetic and Related Models, 6 (2013), 893-917. PDF - D. Coulette, N. Besse,
Multi-water-bag models of ion temperature gradient instability in cylindrical geometry,
Phys. Plasmas, 20 (2013), 052107. PDF - D. Coulette, N. Besse,
Numerical comparisons of gyrokinetic multi-water-bag models,
J. Comput. Phys., 248 (2013), 1-32. PDF - N. Besse,
Global weak solutions for the relativistic waterbag continuum,
Math. Mod. Meth. Appl. Sci., 22 (2012), 1150001. PDF - P. Morel, E. Gravier, N. Besse, R. Klein, A. Ghizzo, P. Bertrand, C. Bourdelle, X. Garbet,
Water-bag modeling of a multispecies plasma,
Phys. Plasmas, 18 (2011), 032512. PDF - N. Besse, Y. Elskens, D. Escande, P. Bertrand,
Validity of quasilinear theory: refutations and new numerical confirmation,
Plasma Phys. Control. Fusion, 53 (2011), 025012. PDF - N. Besse,
On the waterbag continuum,
Arch. Rational Mech. Anal., 199 (2011), 453-491. PDF - N. Besse,
On the Cauchy problem for the gyro-water-bag model,
Math. Mod. Meth. Appl. Sci., 21 (2011), 1839-1869. PDF - R. Klein, E. Gravier, J.-H. Chatenet, N. Besse, P. Bertrand, X. Garbet,
The gyrokinetic Water-bag modeling in toroidal geometry,
Eur. Phys. J. D, 62 (2011), 413-420. PDF - P. Bechouche, N. Besse,
Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system,
ESAIM: M2AN, 44 (2010), 573-595. PDF - R. Klein, E. Gravier, P. Morel, N. Besse, P. Bertrand,
Gyrokinetic water-bag modeling of a plasma column: magnetic moment distribution and finite Larmor radius effects,
Phys. Plasmas, 16 (2009), 082106. PDF - N. Besse, P. Bertrand,
Gyro-water-bag approach in nonlinear gyrokinetic turbulence,
J. Comput. Phys., 228 (2009), 3973-3995. PDF - N. Besse, F. Berthelin, Y. Brenier, P. Bertrand,
The multi-water-bag equations for collisionless kinetic modeling,
Kinetic and Related Models, 2 (2009), 39-90. PDF - E. Gravier, R. Klein, P. Morel, N. Besse, P. Bertrand,
Gyrokinetic-water-bag modeling of low-frequency instabilities in a laboratory magnetized plasma column,
Phys. Plasmas, 15 (2008), 122103. PDF - N. Besse, P. Bertrand, P. Morel, E. Gravier,
Weak turbulence theory and simulation of the gyro-water-bag model,
Phys. Rev. E, 77 (2008), 056410. PDF - N. Besse, P. Bertrand,
Quasi-linear analysis of the gyro-water-bag model,
Europhys. Lett., 83 (2008), 25003. PDF - N. Besse, G. Latu, A. Ghizzo, E. Sonnendrücker, P. Bertrand,
A Wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system,
J. Comput. Phys., 227 (2008), 7889-7916. PDF - X. Garbet, Y. Sarazin, V. Grandgirard, G. Dif-Pradalier, G. Darmet, Ph. Gendrih, P. Angelino, P. Bertrand, N. Besse, E. Gravier, P. Morel, E. Sonnendrücker, N. Crouseilles, J-M. Dischler, G. Latu, E. Violard, M. Brunetti, S. Brunner, X. Lapillonne, T.-M. Tran, L. Villard, M. Boulet,
Beyond scale separation in gyrokinetic turbulence,
Nucl. Fusion, 47 (2007), 1206-1212. PDF - D. Del Sarto, A. Ghizzo, T. Réveillé, N. Besse, P. Bertrand,
Application of a semi-Lagrangian scheme in the relativistic regime of laser interaction with an overdense plasma slab,
Commun. Nonlinear Sci. Numer. Simul., 13 (2008), 59-64. PDF - P. Morel, E. Gravier, N. Besse, R. Klein, A. Ghizzo, P. Bertrand, X. Garbet, Ph. Gendrih, V. Grandgirard, Y. Sarazin,
Gyrokinetic modelling: a multi water bag approach,
Phys. Plasmas, 14 (2007), 112109. PDF - N. Besse,
Convergence of a high-order semi-Lagrangian scheme with propagation of gradients for the Vlasov-Poisson system,
SIAM, J. Numer. Anal., 46 (2008), 639-670. PDF - N. Besse, N.J. Mauser, E. Sonnendrücker,
Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena,
Int. J. Appl. Math. Comput. Sci., 17 (2007), 361-374. PDF - P. Morel, E. Gravier, N. Besse, A. Ghizzo, P. Bertrand,
The water bag model and gyrokinetic applications,
Commun. Nonlinear Sci. Numer. Simul., 13 (2008), 11-17. PDF - A. Ghizzo, D. DelSarto, T. Réveillé, N. Besse, R. Klein,
Self-transparency scenario revisted via the beating of the pump wave and its reflected wave in one dimensional moderately
overdense plasma layer,
Phys. Plasmas, 14 (2007), 062702. PDF - V. Grandgirard, Y. Sarazin, X. Garbet, G. Dif-Pradalier, Ph. Ghendrih, N. Crouseilles, G. Latu, E. Sonnendrücker, N. Besse and P. Bertrand,
Computing ITG turbulence with a full-f semi-Lagrangian code,
Commun. Nonlinear Sci. Numer. Simul., 13 (2008), 81-87. PDF - Y. Sarazin, V. Grandgirard, G. Dif-Pradalier, E. Fleurence, X. Garbet, Ph. Gendrih, P. Bertrand, N. Besse, N. Crouseilles, E. Sonnendrücker, G. Latu, E. Violard,
Impact of large scale flows on turbulent transport,
Plasma Phys. Control. Fusion, 48 (2006), B179-B188. PDF - V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet, P. Ghendrih, G. Manfredi, Y. Sarazin, O. Sauter, E. Sonnendrücker, J. Vaclavik, L. Villard,
A drift-kinetic Semi-Lagrangian 4D code for ion turbulence simulation,
J. Comput. Phys., 217 (2006), 395-423. PDF - N. Besse, M. Mehrenberger,
Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system,
Math. Comp., 77 (2008), 93-123. PDF - N. Besse, D. Kröner,
Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system,
ESAIM: M2AN, 39 (2005), 1177-1202. PDF - N. Besse, J. Segré, E. Sonnendrücker,
Semi-Lagrangian schemes for the two-dimensional Vlasov-Poisson system on unstructured meshes,
Trans. Theo. Stat. Phys., 34 (2005), 311-332. PDF - N. Besse,
Convergence of a semi-Lagrangian scheme for the one-dimensional Vlasov-Poisson system,
SIAM J. Numer. Anal., 42 (2004), 350-382. PDF - N. Besse, E. Sonnendrücker,
Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space,
J. Comput. Phys., 191 (2003), 341-376. PDF.
Papers published in conference proceedings and chapters of book
- N. Besse, F. Filbet, M. Gutnic, I. Paun, E. Sonnendrücker,
An adaptive numerical method for the Vlasov equation based on a multiresolution analysis,
In Numerical Mathematics and Advanced Applications, Eds F. Brezzi, A. Buffa, S. Escorsaro, A. Murli, Springer, (2003), 437-446. PDF
Habilitation à diriger des recherches
- N. Besse,
Contributions à l'analyse mathématique et à l'approximation numérique en physique des plasmas,
Université Henri Poincaré, Nancy, 2009.
PhD Thesis
- N. Besse,
Etude mathématique et numérique de l'équation de Vlasov non linéaire sur des maillages non structurés de l'espace des phases,
Publication IRMA, Université Louis Pasteur, Strasbourg, 2003.
Technical Reports
- N. Besse,
Etude d'une méthode stochastique pour la résolution de l'opérateur de collision de Fokker-Planck ,
Rapport CEA, CEA/DAM/DIF/DCSA/SNEC, N72/DO, 2000. - V. Grandgirard, N. Besse, E. Sonnendrücker,
Amélioration des schémas numériques semi-Lagrangiens associés à la résolution des équations de Vlasov non-linéaires 4D pour l'étude de la turbulence plasma ,
Rapport CEA, CEA/CADARACHE/DRFC/SIPP/GTHM, PHY/NTT-2003.013, 2003.
Research
- Détails
Research Interests
My research interests are mathematical modelling and methods, numerical analysis and scientific computing around nonlinear PDEs which arise in plasma physics and fluid mechanics:
- Nonlinear Vlasov equations (charged particles transport processes, electromagnetic versus gravitational interactions)
- Geometric reduction of Vlasov equations by geometric Liouville invariants (waterbags type models, multi–fluids models)
- Quasilinear theory, models for plasma turbulence (Hamiltonian versus dissipative, resonant wave–particle interaction)
- Hydrodynamics and Magneto–Hydrodynamics models (Incompressible Euler equations, MHD, XMHD)
- Semi-classical limits of nonlinear Schrödinger equations (WKB, singular interaction potential)
- New (deterministic & stochastic) Lagrangian formulation of fluid mechanics on flat and curved spaces
- Geometric Lagrangian formulation of fluid mechanics with applications for mathematical and numerical analysis
- Numerical schemes of arbitrary high order for fluid mechanics with applications for finite-time singularities (blowup)
Teaching
- Détails
Lectures
- I teach mathematics and numerical analysis at Université Côte d'Azur at level L1, M1 and M2.
- I give lectures on advanced topics in PDEs analysis at the Doctoral School SFA such as collisionless kinetic equations Part 1 & Part 2.
PhD/Postdoc Proposals
- Détails
PhD Proposal:
to be continued ...
Post-doctoral Proposal:
to be continued ...
UMR LAGRANGE
Observatoire de la Côte d’Azur
Boulevard de l’Observatoire
CS 34229 - F 06304 NICE Cedex 4
Tél. : +33 (0)4 92 00 30 11
Fax : +33 (0)4 92 00 30 33
